Inverse method for identifying the underlying crack distribution in plates with random strengths

    Authors

    Y. Ahn; D. W. Nicholson; M. C. Wang;P. Ni

    Comments

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    Abbreviated Journal Title

    Acta Mech.

    Keywords

    ENERGY; Mechanics

    Abstract

    In the current investigation we seek to identify the underlying crack number and crack length distributions in brittle plates with a known strength distribution. The inverse problem in probabilistic fracture mechanics is defined, and the numerical procedure to solve the inverse problem is constructed. The simulation process of generating simulated plates containing simulated random cracks is elaborated. The maximum strain energy release rate criterion (G(max)) is applied to each simulated random crack to find the crack strength. The strength of the simulated plate is equated to the strength of the weakest simulated crack in the plate based on the weakest link notion. The underlying crack number and crack length distributions are obtained by minimizing the difference between the simulated plate strengths and the known plate strengths. The gamma lognormal and two-parameter Weibull distributions are employed for the underlying crack length distribution, and are compared in order to identify the best choice. Numerical examples demonstrate that the three PDFs are all acceptable for reasons to be explained. In the appendix, the direct problem in probabilistic fracture mechanics is presented as part of the demonstration of a method for using the crack distribution identified in the inverse problem to predict the strength and the probability of fracture in a practical application.

    Journal Title

    Acta Mechanica

    Volume

    144

    Issue/Number

    3-4

    Publication Date

    1-1-2000

    Document Type

    Article

    Language

    English

    First Page

    137

    Last Page

    154

    WOS Identifier

    WOS:000166375400002

    ISSN

    0001-5970

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